Proposition 1.([1]}) Given a spanning forest subgraph \(\mathcal {F}:=(\mathcal {V},\mathcal {E}_F)\)  of a connected graph \(\mathcal {G}:=(\mathcal {V},\mathcal {E})\) , there exists at least one spanning tree subgraph of \(\mathcal {G}\) , expressed as \(\mathcal {T}:=(\mathcal {V},\mathcal {E}_T)\) , such that \(\mathcal {E}_F \subseteq \mathcal {E}_T \subseteq \mathcal {E}\) .
